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Thread: Determining plane based on lines in R^3

  1. #1
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    Question Determining plane based on lines in R^3

    For the question below, what is the strategy for determining the position and direction vectors of the plane P?

    Determining plane based on lines in R^3-screen-shot-2019-09-20-2.28.09-pm.png

    In order to derive the 2 direction vectors, I would need to know 3 points on the plane, and then compute the difference. The points can be determined by evaluating either line A or line B at some point t. I'm not sure which points to use however. Help?

    As for the position vector, I think this will rely on how I determine the direction vectors. I also need help with this.
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    Re: Determining plane based on lines in R^3

    Quote Originally Posted by otownsend View Post
    For the question below, what is the strategy for determining the position and direction vectors of the plane P?
    Click image for larger version. 

Name:	Screen Shot 2019-09-20 at 2.28.09 PM.png 
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    In order to derive the 2 direction vectors, I would need to know 3 points on the plane, and then compute the difference. The points can be determined by evaluating either line A or line B at some point t. I'm not sure which points to use however. Help?
    As for the position vector, I think this will rely on how I determine the direction vectors. I also need help with this.
    First we need to know that the lines intersect: $(0,0,1)\in\ell_1(t)\cap\ell_2(s)$
    $\left<1,2,3,\right>$ is the direction vector of $\ell_1(t)$ and $\left<-1,1,1,\right>$ is the direction vector of $\ell_2(s)$
    The normal to the plane is $\left<1,2,3,\right>\times\left<-1,1,1\right>$
    You have a point and a normal write the equation of the plane.
    Thanks from topsquark and otownsend
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  3. #3
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    Re: Determining plane based on lines in R^3

    Nvm. Thank you for your help!
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